As for autocorrelation, given the sparseness of the data points in the time domain, maybe the autocorrelation is very weak? If autocorrelation is strong enough to violate assumption of independence, why not sub-sample (and iteratively resample) the data so that they are independent?

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I just read the paper and it looks like an important step forward in terms of (a) quantifying uncertainty in proxy reconstructions, and more importantly (b) explicitly laying out the assumptions which are made in these proxy temperature records.

However, this is probably the most important paragraph:

Although we focus on presenting a methodology for the uncertainty analysis, it is worth to mention that the reconstruction is only robust under the given assumptions. However, there is a possibility of violations of those assumptions. For example, the increase of CO2 may accelerate the growth of trees (e.g. MBH99), so that makes the recent relationship between tree rings and temperature differ from the past. If this is true, it will break the important statistical assumption of a stationary relationship between temperature and proxies. In addition, because the proxy records end in 1980, the warm decades since then cannot be reconstructed. Hence, based on the stationarity assumption, we use the instrumental data for this period.

In other words, these error estimates are only good when the proxies are linear and stationary. Has this ever been shown for the tree rings that they use in this paper?

This might simply be the result of my sloppy data-point grabbing (see below) However I took the residuals off Fig 1 and put them into Kurt Annen’s ARMA add-in for MSExcel. This selected p=5 q=4 on the basis of the Akaike Information Criterion. The significance of the terms seemed quite interesting:
The AR2 term p=0.20
The MA2 term p=0.03
with AR4 p=0.005 and MA4 0.10
I remember from a previous discussion on ‘spurious regression’ how the inclusion of an MA term altered the perspective and wondered if it might also be the case here. A ten period ‘forecast’ plot based on the the full ARMA is qualitatively very different from the one generated from an AR2 analysis.
-My grotty point-grabbing might be contributing to all this: my points have a trend (0.04 degrees in 100 years) and add up to 0.13

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[…] Bo Li et al has already discussed certain data issues in depth, but the 11/18/07 general discussion Li et al 2007 never really got off the ground. (See also a few comments by Jean S and others in an unrelated CA […]